A New Class of L2-Stable Schemes for the Isentropic Euler Equations on Staggered Grids

Staggered schemes for compressible flows are highly non linear and the stability analysis has historically been performed with a heuristic approach and the tuning of numerical parameters [12]. We investigate the L-2-stability of staggered schemes by analysing their numerical diffusion operator. The analysis of the numerical diffusion operator gives new insight into the scheme and is a step towards a proof of linear stability or stability for almost constant initial data. For most classical staggered schemes [9-11, 14], we are able to prove the positivity of the numerical diffusion only in specific cases (constant sign velocities). We then propose a class of linearly L-2-stable staggered schemes for the isentropic Euler equations based on a carefully chosen numerical diffusion operator. We give an example of such a scheme and present some first numerical results on a Riemann problem.